Documentation for RPNM Series Calculators March 19, 1992 The RPNM series of Calculators is a group of calculator programs that were produced by Harry Smith of Saratoga CA. These calculators are unusual in that they not only provide very extended precision arithmetic (numbers with several thousand digits), but they also permit the user to define the precision for the calculator (up to the limit of your particular system's memory). The ability to set the calculator's precision is desirable to control the speed of the calculations. The calculators also utilize Reverse Polish Notation (RPN), thus the name of the series is RPNMx, for RPN Multiple precision; and x is used to distinguish between the different individual calculators of the series. There are currently three different calculators in the RPNMx series: RPNMI - Integer RPNMF - Floating point RPNMS - Scientific The Scientific calculator (RPNMS) is the most general, however the primary reason for different versions, is to permit more digits of precision when fewer features are required for control or arithme- tic functions. For example, the Scientific calculator can perform integer calculations but is limited to about 1/3 as many digits as the Integer calculator (RPNMI). On the other hand, the Scientific calculator can produce the transcendental functions normally required for mathematical calculations; e.g., sin, cos, log, ln, e to the x power, or x to the y power, etc.; and of course it operates in floating point. All of the calculators have the following basic features: * RPN arithmetic utilizing a four register stack (Plus secondary storage for 2 more registers) * Some programmability called "The Learned Line" (Admittedly limited but quite useful) * Random number generator * Radix control to permit numeric bases other than decimal * Extensive Operator Control features to enhance effective and time efficient utilization: * Display control - permit suppression of intermediate results when not needed (Note: Recall that a register may have thousands of digits to display!) * Separators to group display digits arbitrarily e.g., 12,345,678 instead of 12345678 for maybe 4000 digits. or 123,4567,89AB,CDEF when using the Hexadecimal base * Control of display prompts and/or bells * Disk I/O capability to permit the calculator to be operated by scripts or for off-line control. This is very useful for two reasons in particular: (1) Scripts (or files of operations) allows an operator sequence to be repeated exactly; thus, a sequence can be developed, changed, compared, and saved in as many variations as desired. (2) Since the time of some calculations may be quite long, the system can be controlled while the user is away (say overnight or at work). * Other features peculiar to the floating point or scientific calculator e.g., although the floating point calculator has less preci- sion it can operate on numbers as large as 10 to the 39 thousandth power! The dynamic range of floating point is extraordinary and is worth a special note. Consider the dynamic range of the IBM 370 double precision values. It is about 10 to + or - 75'th power; which is about the same as other major main frame computers. So how big is 10 to 39,000'th power? Well, for example: The distance to other stars is usually thought to be so large that we use light years (LY) rather than miles to say how far they are. The distance to the nearest star is about 4 LY; 4 is a small number but that is why we used ly in the first place, because each LY is about 6,000,000,000,000 miles, which is a big number. On the other hand, the distance across an atom is such a small length (approximately 0.000000004 inches) that we use it to measure small distances (this length is called an angstrom). Now back to the stars. If the distance to a star is large, the distance to galaxies is much larger. Our nearest galactic neighbor is about 750,000 LY; and the far ones are so far that they are measured with megaparsecs (Mpc), which are approximately 3,260,000 LY each. A far galaxy may be more than 3000 Mpc away. Therefore, it seems fair to say that the distance to a far galaxy by almost any measure would be a big number; but how far is a far galaxy in angstrom units? Well, 3000 Mpc, times 3,260,000 LY per Mpc, times 6,000,000,000,000 miles per LY, times 63,000 inches per mile, times 254,000,000 angstroms per inch is 10 to the 36'th angstroms to a far galaxy (approximately). Another example of a large number might be the number of atoms in the universe. This has been estimated by some people to be 10 to the 72'nd power. So the dynamic range of this calculator can handle "big" numbers (10 to the 39,000'th power) as well as "small" numbers (10 to the -39,000'th power). Can you think of an example of a value of something in the real world that is "big" or "small"? * The square of the distance to a far galaxy is approximately 10^36 * 10^36 = 10^72 * The volume of the known universe in cubic angstroms units is 4/3 Pi * (10^36)^3 = 10^109 approximately Wayne Fuqua

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